Application of a wavelet-Galerkin method to the forward problem resolution in fluorescence diffuse optical tomography.

Fluorescence diffuse optical tomography is a powerful tool for the investigation of molecular events in studies for new therapeutic developments. Here, the emphasis is put on the mathematical problem of tomography, which can be formulated in terms of an estimation of physical parameters appearing as a set of Partial Differential Equations (PDEs). The standard polynomial Finite Element Method (FEM) is a method of choice to solve the diffusion equation because it has no restriction in terms of neither the geometry nor the homogeneity of the system, but it is time consuming.

Model reduction using wavelet multiresolution technique applied to fluorescence diffuse optical tomography.

Fluorescence diffuse optical tomography is a powerful tool for the investigation of molecular events in studies for new therapeutic developments. Here, the stress is put on the mathematical problem of tomography, which can be formulated in terms of an estimation of physical parameters appearing as a set of partial differential equations and solved by the finite element method. This method is well known to be time consuming, and our principal objective is to reduce the model in order to speed up computation.

Reconstruction method and optimal design of an interferometric spectrometer.

In this paper, we present a method to estimate the power spectral distribution of a source from input data acquired by an interferometric-based spectrometer. Our spectrometer shows distortions in the fringe pattern and a lack of data, making it impossible to apply the Fourier transform approach, which is the gold standard as a spectral recovery method for interferometric spectrometers. We combined linear inverse problem solving and iterative methods instead, considering that each detector of the spectrometer has a specific and known spectral response.